Initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity

Abstract

In this paper, we study the initial boundary value problem for a class of semilinear pseudo-parabolic equations with logarithmic nonlinearity. By using the logarithmic Sobolev inequality and a family of potential wells, we obtain the existence of global solution, blow-up at +∞ and behavior of vacuum isolation of solutions. On the other hand, the asymptotic behavior of solutions is also discussed. Our result implies that the polynomial nonlinearity is important for the solutions of such kinds of semilinear pseudo-parabolic equations to be blow-up in finite time.